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Home » Let the number of reflecting telescopes be $ r = 11 $. - Simpleprint

Let the number of reflecting telescopes be $ r = 11 $. - Simpleprint

📅 March 15, 2026 👤 scraface

Mar 15, 2026

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\(a = 2\), \(b = 1012\), then \(x = (2+1012)/2 = 507\), \(y = (1012 -...
Check: \(507^2 - 505^2 = (507-505)(507+505) = 2 \cdot 1012 = 2024\), c...
Another: \(m = -1\), \(n = -506\): \(x = -507/2\), not integer — wait!...
But when we list all divisor pairs \((m,n)\) with \(mn = 506\), we inc...
No: for each factorization, we get a point. But since \(m\) and \(n\)...
But each pair \((m,n)\) with \(mn = 506\) gives a unique \((x,y)\)?
Suppose \((m,n)\) and \((m',n')\) give same \((x,y)\): then \(m + n =...
From second: \(n = m + y\), substitute: \(m(m + y) = 506\), and \(m(n'...
Instead, note that \(x = m + n\), \(y = n - m\), so \(x^2 - y^2 = (m+n...
And different \((m,n)\) may give same \((x,y)\)?

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